Bayesian partition model for identifying hypo- and hyper- methylation
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This dissertation introduces MethyBayes, a full Bayesian partition model for identifying hypo- and hypermethylated loci. The main interest of study on DNA methylation data is to test the methylation difference under two conditions of biological samples. However, the high cost and complexity of this sequencing experiment limits the number of biological replicates, which brings challenges to the development of statistical methods. Current available methods can only provide binary output of a locus being differentially methylated or not, and an extra step based on the sign of test statistics is always needed to further identify hypo- and hyper-methylation. In our proposed full Bayesian partition model, we introduce a latent variable to indicate membership of methylation for each locus, and assign priors for equal-, hypo- and hypermethylation loci separately. One-step output of each locus being either equal-, hypo- or hyper-methylated locus is produced without further post-hoc analysis. We also conduct simulation study and real data analysis including bioinformatic analysis to show that the proposed full Bayesian partition model outperforms existing methods in terms of power while maintaining a low false discovery rate. This dissertation also introduces a non-parametric Bayesian change point model to estimate parameters of a sequence of observations that experiences changes at unknown times, which also involves the identification of these change points. We use a latent variable to represent change point status. A Dirichlet prior is applied to capture the cluster effect without pre-knowledge of the number of clusters. We illustrate the proposed Bayesian change point model via normal distribution in continuous case and Poisson distribution in discrete case.
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